The heterogeneous catalytic asymmetric hydrogenation of the C=C bond resulting in optically active product has been a challenge since decades. Such products can arise in enantio- and in diastereoselective reactions depending on whether the prochiral compound is hydrogenated with a chirally modified catalyst or the substrate itself contains the source of chirality in the form of a chiral moiety. The common step in these reactions is the stereodifferentiating hydrogen uptake on the surface of the metal, first of all on that of the Pd. In our laboratory, experiences were collected in the last two decades for both reaction types. The asymmetric C=C hydrogenation of α,β-unsaturated ketones was studied with modified catalysts in the presence of chiral auxiliaries, like the (S)-proline. The latter turned out to be a diastereoselective reaction. Beside the well-known cinchona alkaloids a vinca alkaloid and diphenyl methyl pyrrolidine methanol also were applied as chiral modifiers. The afforded e.e. (enantiomeric excess) values were in most cases moderate, which could be explained among others with the relatively low reaction rates. In comparison with the Pt/cinchona system, large amount of modifier was necessary for the Pd catalyst, and this resulted in the lower reaction rates. The asymmetric hydrogenation of the C=C bond was studied with optically active dehydroamino acid amides, prolineamides of picolinic, nicotinic and pyrrole acetic acids and pyridoin in diastereoselective reactions.